Python RigidBody.inertia方法代码示例

# 需要导入模块: from sympy.physics.mechanics import RigidBody [as 别名]
# 或者: from sympy.physics.mechanics.RigidBody import inertia [as 别名]
def test_rigidbody():
    m, m2, v1, v2, v3, omega = symbols('m m2 v1 v2 v3 omega')
    A = ReferenceFrame('A')
    A2 = ReferenceFrame('A2')
    P = Point('P')
    P2 = Point('P2')
    I = Dyadic([])
    I2 = Dyadic([])
    B = RigidBody('B', P, A, m, (I, P))
    assert B.mass == m
    assert B.frame == A
    assert B.masscenter == P
    assert B.inertia == (I, B.masscenter)

    B.mass = m2
    B.frame = A2
    B.masscenter = P2
    B.inertia = (I2, B.masscenter)
    assert B.mass == m2
    assert B.frame == A2
    assert B.masscenter == P2
    assert B.inertia == (I2, B.masscenter)
    assert B.masscenter == P2
    assert B.inertia == (I2, B.masscenter)

    # Testing linear momentum function assuming A2 is the inertial frame
    N = ReferenceFrame('N')
    P2.set_vel(N, v1 * N.x + v2 * N.y + v3 * N.z)
    assert B.linear_momentum(N) == m2 * (v1 * N.x + v2 * N.y + v3 * N.z)

# 需要导入模块: from sympy.physics.mechanics import RigidBody [as 别名]
# 或者: from sympy.physics.mechanics.RigidBody import inertia [as 别名]
def test_aux():
    # Same as above, except we have 2 auxiliary speeds for the ground contact
    # point, which is known to be zero. In one case, we go through then
    # substitute the aux. speeds in at the end (they are zero, as well as their
    # derivative), in the other case, we use the built-in auxiliary speed part
    # of Kane. The equations from each should be the same.
    q1, q2, q3, u1, u2, u3  = dynamicsymbols('q1 q2 q3 u1 u2 u3')
    q1d, q2d, q3d, u1d, u2d, u3d = dynamicsymbols('q1 q2 q3 u1 u2 u3', 1)
    u4, u5, f1, f2 = dynamicsymbols('u4, u5, f1, f2')
    u4d, u5d = dynamicsymbols('u4, u5', 1)
    r, m, g = symbols('r m g')

    N = ReferenceFrame('N')
    Y = N.orientnew('Y', 'Axis', [q1, N.z])
    L = Y.orientnew('L', 'Axis', [q2, Y.x])
    R = L.orientnew('R', 'Axis', [q3, L.y])
    R.set_ang_vel(N, u1 * L.x + u2 * L.y + u3 * L.z)
    R.set_ang_acc(N, R.ang_vel_in(N).dt(R) + (R.ang_vel_in(N) ^
        R.ang_vel_in(N)))

    C = Point('C')
    C.set_vel(N, u4 * L.x + u5 * (Y.z ^ L.x))
    Dmc = C.locatenew('Dmc', r * L.z)
    Dmc.v2pt_theory(C, N, R)
    Dmc.a2pt_theory(C, N, R)

    I = inertia(L, m / 4 * r**2, m / 2 * r**2, m / 4 * r**2)

    kd = [q1d - u3/cos(q3), q2d - u1, q3d - u2 + u3 * tan(q2)]

    ForceList = [(Dmc, - m * g * Y.z), (C, f1 * L.x + f2 * (Y.z ^ L.x))]
    BodyD = RigidBody()
    BodyD.mc = Dmc
    BodyD.inertia = (I, Dmc)
    BodyD.frame = R
    BodyD.mass = m
    BodyList = [BodyD]

    KM = Kane(N)
    KM.coords([q1, q2, q3])
    KM.speeds([u1, u2, u3, u4, u5])
    KM.kindiffeq(kd)
    kdd = KM.kindiffdict()
    (fr, frstar) = KM.kanes_equations(ForceList, BodyList)
    fr = fr.subs({u4d: 0, u5d: 0}).subs({u4: 0, u5:0})
    frstar = frstar.subs({u4d: 0, u5d: 0}).subs({u4: 0, u5:0})

    KM2 = Kane(N)
    KM2.coords([q1, q2, q3])
    KM2.speeds([u1, u2, u3], u_auxiliary=[u4, u5])
    KM2.kindiffeq(kd)
    (fr2, frstar2) = KM2.kanes_equations(ForceList, BodyList)
    fr2 = fr2.subs({u4d: 0, u5d: 0}).subs({u4: 0, u5:0})
    frstar2 = frstar2.subs({u4d: 0, u5d: 0}).subs({u4: 0, u5:0})

    assert fr.expand() == fr2.expand()
    assert frstar.expand() == frstar2.expand()

# 需要导入模块: from sympy.physics.mechanics import RigidBody [as 别名]
# 或者: from sympy.physics.mechanics.RigidBody import inertia [as 别名]
def test_rigidbody():
    m = Symbol('m')
    A = ReferenceFrame('A')
    P = Point('P')
    I = Dyadic([])
    B = RigidBody()
    assert B.mass == None
    assert B.mc == None
    assert B.inertia == (None, None)
    assert B.frame == None

    B.mass = m
    B.frame = A
    B.cm = P
    B.inertia = (I, B.cm)
    assert B.mass == m
    assert B.frame == A
    assert B.cm == P
    assert B.inertia == (I, B.cm)

# 需要导入模块: from sympy.physics.mechanics import RigidBody [as 别名]
# 或者: from sympy.physics.mechanics.RigidBody import inertia [as 别名]
def test_rigidbody():
    m, m2 = symbols('m m2')
    A = ReferenceFrame('A')
    A2 = ReferenceFrame('A2')
    P = Point('P')
    P2 = Point('P2')
    I = Dyadic([])
    I2 = Dyadic([])
    B = RigidBody('B', P, A, m, (I, P))
    assert B.mass == m
    assert B.frame == A
    assert B.mc == P
    assert B.inertia == (I, B.mc)

    B.mass = m2
    B.frame = A2
    B.mc = P2
    B.inertia = (I2, B.mc)
    assert B.mass == m2
    assert B.frame == A2
    assert B.mc == P2
    assert B.inertia == (I2, B.mc)

# 需要导入模块: from sympy.physics.mechanics import RigidBody [as 别名]
# 或者: from sympy.physics.mechanics.RigidBody import inertia [as 别名]
def test_rolling_disc():
    # Rolling Disc Example
    # Here the rolling disc is formed from the contact point up, removing the
    # need to introduce generalized speeds. Only 3 configuration and three
    # speed variables are need to describe this system, along with the disc's
    # mass and radius, and the local graivty (note that mass will drop out).
    q1, q2, q3, u1, u2, u3 = dynamicsymbols('q1 q2 q3 u1 u2 u3')
    q1d, q2d, q3d, u1d, u2d, u3d = dynamicsymbols('q1 q2 q3 u1 u2 u3', 1)
    r, m, g = symbols('r m g')

    # The kinematics are formed by a series of simple rotations. Each simple
    # rotation creates a new frame, and the next rotation is defined by the new
    # frame's basis vectors. This example uses a 3-1-2 series of rotations, or
    # Z, X, Y series of rotations. Angular velocity for this is defined using
    # the second frame's basis (the lean frame).
    N = ReferenceFrame('N')
    Y = N.orientnew('Y', 'Axis', [q1, N.z])
    L = Y.orientnew('L', 'Axis', [q2, Y.x])
    R = L.orientnew('R', 'Axis', [q3, L.y])
    R.set_ang_vel(N, u1 * L.x + u2 * L.y + u3 * L.z)
    R.set_ang_acc(N, R.ang_vel_in(N).dt(R) + (R.ang_vel_in(N) ^ R.ang_vel_in(N)))

    # This is the translational kinematics. We create a point with no velocity
    # in N; this is the contact point between the disc and ground. Next we form
    # the position vector from the contact point to the disc mass center.
    # Finally we form the velocity and acceleration of the disc.
    C = Point('C')
    C.set_vel(N, 0)
    Dmc = C.locatenew('Dmc', r * L.z)
    Dmc.v2pt_theory(C, N, R)
    Dmc.a2pt_theory(C, N, R)

    # This is a simple way to form the inertia dyadic.
    I = inertia(L, m / 4 * r**2, m / 2 * r**2, m / 4 * r**2)

    # Kinematic differential equations; how the generalized coordinate time
    # derivatives relate to generalized speeds.
    kd = [q1d - u3/cos(q3), q2d - u1, q3d - u2 + u3 * tan(q2)]

    # Creation of the force list; it is the gravitational force at the mass
    # center of the disc. Then we create the disc by assigning a Point to the
    # mass center attribute, a ReferenceFrame to the frame attribute, and mass
    # and inertia. Then we form the body list.
    ForceList = [(Dmc, - m * g * Y.z)]
    BodyD = RigidBody()
    BodyD.mc = Dmc
    BodyD.inertia = (I, Dmc)
    BodyD.frame = R
    BodyD.mass = m
    BodyList = [BodyD]

    # Finally we form the equations of motion, using the same steps we did
    # before. Specify inertial frame, supply generalized speeds, supply
    # kinematic differential equation dictionary, compute Fr from the force
    # list and Fr* fromt the body list, compute the mass matrix and forcing
    # terms, then solve for the u dots (time derivatives of the generalized
    # speeds).
    KM = Kane(N)
    KM.coords([q1, q2, q3])
    KM.speeds([u1, u2, u3])
    KM.kindiffeq(kd)
    KM.kanes_equations(ForceList, BodyList)
    MM = KM.mass_matrix
    forcing = KM.forcing
    rhs = MM.inv() * forcing
    kdd = KM.kindiffdict()
    rhs = rhs.subs(kdd)
    assert rhs.expand() == Matrix([(10*u2*u3*r - 5*u3**2*r*tan(q2) +
        4*g*sin(q2))/(5*r), -2*u1*u3/3, u1*(-2*u2 + u3*tan(q2))]).expand()